A simplified one dimensional stick model for earthquake response analysis of framed buildings

A procedure for modifying an existing model that resembles a two dimensional moment resisting frame of a building for its dynamic behavior to develop a one dimensional stick model is presented. The procedure is assumed to be applicable for both time domain and response spectrum analysis for earthquake base excitation such as (El_Centro) that acts on the original 2D frame of the building. The modified stick model is assumed to compose of an assemblage of a series of two node cantilever beams having two degrees of freedom per node, the rotational degree of freedom at each node is further condensed at element level resulting in a new stiffness and mass matrices taking into account the effects of those rotations. Different correction factors are implemented for the exterior and interior columns in addition to the number of floors of the original 2-dimensional frame of the building in each direction. The developed procedure is then implemented in time domain and response spectrum analysis using a computer program especially coded and written for the purpose of the study on the basis of MTAB. For each case study of multi-story building, the natural time period and the resulting base shear and drifts which are predicted by the proposed stick model are evaluated and compared with other existing modeling techniques. Though a good agreement of the natural time periods of the building frames between the proposed modeling technique and other methods was found but, the responses were found to be –in general- higher than those of the conventional 2D frame. While, the drifts as expected by the stick model seem to be lower than those of the conventional 2D frame modeling techniques (the finite element based on SAP2000).